My DH has similar traits and he has adhd. Before we moved in together, his garden was knee high weeds (and probably still would be, if I hadn’t got involved). If he doesn’t need a space, he can’t see the point in fixing it. Even now, we have many started not finished projects which drive me crazy but I keep them more or less in check with putting plans in place and managing them, paying out and doing stuff myself. It’s exhausting, but it’s part of who he is and I love him dearly regardless.
Your neighbour doesn’t have any form of control measures, for want of a better term, so he sees no reason to fix anything. My DH saw his house as a roof over his head but not a home. He had plenty of money, but slept on a mattress on the floor and had no curtains for instance. I do think your neighbour sounds like an extreme version of my DH. I’d be willing to bet his house inside is untidy and full of “stuff”, but clean.
Only mentioning all this to try and help you find a way forward. I think you need to tap into what his “control measures” might be. Whether that’s a proper sit down conversation where you share concerns and ask if you can help/can he make a plan - which you would need to put a timing to, and review (almost like old fashioned smart targets), or whether it’s getting environmental health involved over rodents in the garden. Honestly, I don’t have huge confidence in either working but it’s worth a shot.
Re ticks btw - they are carried into gardens by animals, most likely cats and foxes. They need animals to survive, so although the long weeds provide a launching pad for them to brush against your cat, something else is facilitating their travel. Unless neighbour kids are in the garden walking amongst the weeds, or have cats carrying them about, they won’t get tick bites.
Final thing, having lived next door to a v responsible neighbour who had decking and consequently rats - if you call anyone out about rats, agree that the first thing they’ll do is look to your decking.